While nomograms are discussed in detail elsewhere (chapter “Nomograms”) a brief discussion in this section is pertinent. Mathematical descriptions and relationships that can be used to characterize voiding and degrees of obstruction have evolved significantly. Initially, the relationship between pressure and flow was based on the presupposition that the bladder and urethra functioned under basic rigid tube and spherical hydrodynamic principles [1]. Under this model of a rigid pipe, for a given pressure (p) the cross sectional area (A) of the tube determines flow rate (Q).
This is a simplified variation of Bernoulli’s equation [2]. However, a large assumption made in this simple rigid model is that all pressure is converted to flow velocity. This model fails to take into consideration the distensibility, or elasticity of the urethra. In the 1960s a distensible and collapsible system was described where pressure is required to distend the urethral lumen [3, 4]. Since even with a fully relaxed pelvic floor, the urethra will still be collapsed. Pressure-energy is then consumed during this process of opening the urethra during voiding and is not converted to flow. This “energy”, or elasticity, has been termed the minimal urethral opening pressure (p _muo ) or now the minimum voiding pressure (p _det.min.void ) in International Continence Society (ICS) terminology [5]. So now flow is dependent on the cross sectional area and the urethral opening pressure, which then modifies the equation:
According to this principle, the flow of urine will only occur when intrinsic bladder pressure equals the intrinsic urethral pressure [2]. The p_det.min.void, is very important for diagnosing obstruction, as it is the minimum voiding pressure documented during measurable flow and may differ from the “opening pressure” or “closing pressure” [5]. It is typically measured at the end of voiding, with strong consideration to both equipment flow delay and the draining of the distal urethra (approximately the last 5–10 mL and/or flow rate less than 2 mL/s). This number should always be read on the original tracings and clinicians should avoid the temptation to allow the software to read these without validation by the physician [6].

Although it was recognized that the urethra was not a rigid pipe, it was still initially assumed that once the urethra was opened, it could be treated as a rigid structure. This assumption was based on the interpretation of fluoroscopic images that showed that the urethra did not appear to have any major changes in size and/or shape during voiding. However, even when the shape is unchanged, the distensible tube is still fundamentally different from a rigid one, because the fluid is still under the elastic laws of the urethral wall [2]. From this, it follows that these elastic laws, which vary in significance along the urethra, control the flow rate. So for a fixed pressure, the maximum flow rate is controlled by the area with the combination of least elasticity and smallest lumen of the urethra, termed the flow controlling zone (FCZ) [7]. The FCZ is the area of highest pressure within the urethra, and not necessarily the area with the smallest lumen [8].

As summarized by Schaefer, “. . .an important difference between flow in a rigid and an elastic outlet is related to the flow controlling zone. In a rigid system the whole length of the bladder outlet from the bladder neck to the meatus contributes to the fluid energy losses, and the size of the meatal exit area controls the flow rate. In an elastically distensible system the pressure/flow rate relation is governed by the size and elasticity of a flow rate controlling zone, which in general is not the exit area. Physiologically, this zone is located at the genitourinary diaphragm, so that only the fluid energy losses upstream from there can affect the flow rate, and the meatus controls only the exit velocity of the urinary stream” [2].

In addition, a few properties are considered and have been proven to be negligible to simplify the above equations: flow is steady through a constant cross-sectional area, fluid viscosity and other energy losses are negligible, and outlet pressure is the same near the beginning and end of voiding. If negligible, the relationship between pressure and flow is controlled by the elasticity (p_det.min.void) and the urethral cross sectional area (A) as previously shown. In men, this is at the junction of the prostatic and membranous urethra, while in women, this is at the mid-point of the urethra [8]. Men with a longer urethra should have statistically significant higher energy losses according to the above hydrodynamic principles. But the FCZ is close to bladder and controls the flow rate. The urethra above this area does result in energy losses but given its relatively short length, it is more akin to the length of the female urethra, and these short distances have proven negligible and are not included in the above equations [2]. The exact equations and explanations for this are beyond the scope of this chapter.

With this now better understood, Griffiths set out to determine and measure the properties of the this flow controlling zone during voiding. For a known urethra, he did near continuous plotting of corresponding Q’s and p’s during an entire void, and plotted this on a detrusor pressure-flow rate graph. The relationship representing the detrusor pressure needed to propel urine through a urethra at a particular flow rate he termed the urethral resistance relation (URR), and it is dependent only on the urethral mechanical properties [8]. In other words, for a urethra with constant mechanical properties, as the flow rate increases, so must the intrinsic bladder pressure.

Unfortunately, this required finding multiple points to plot that were all affected significantly by the inherent flow delay and other artifacts in urodynamics. Today, this can be plotted as a continuous line on a pressure-flow chart, but initially required multiple individual points that were then connected by a line. The passive urethral resistance relation (PURR) was described by Schafer in the 1980s and was the first attempt to simplify the URR [2, 9]. The PURR is fundamentally based on Griffith’s work of urethral resistance relation (URR), but describes the relationship between pressure and flow during the period of lowest urethral resistance. This requires a computer program to calculate the curve based on the continuous pressure flow graph in attempt to simulate the pressure-flow relationship if complete urethral relaxation, or the largest possible A, occurred during the entire void (Fig. 1). The purpose of this is to most closely evaluate the true morphology of a particular bladder outlet, in order to evaluate for inherent obstruction. Of note, deviations from the PURR are considered to be from the variable contractions of the external sphincter during voiding (active) or slow distensibility of the urethra (passive) [10].

Subsequently, Schaefer noted that the curve of the PURR was of only secondary importance clinically and required a computer to calculate, so to further simplify, the PURR curve was traded for a straight line, and termed the linear PURR or LinPURR (Fig. 1). The two points at the ends of this line are the p_det.min.void, or the lowest pressure where flow starts or stops, and p_det.Qmax [6]. From these lines the Schaeffer nomogram was derived. In separate but similar work, Abrams and Griffiths developed the bladder outlet obstruction index (BOOI), previously referred to as the AG number, which was initially derived from pressure-flow studies in 117 men >55 years old with suspected prostatic obstruction [11]. The equation was derived from the line dividing the obstructed from the equivocal range on a scatter plot of the Abrams-Griffiths study:
where 2 is the slope of the line. This equation became the basis for the ICS nomogram in 1997 [5], and cut off values gleaned from prior works were established:

It should be noted that to make a diagnosis of bladder obstruction (BOOI > 40) p_det must be at least be 40 cm H₂O.

The dynamics of micturition involve both the bladder outlet and detrusor function and equations like the BOOI formula does not take into account bladder contractility. Shafer described the detrusor muscle as the source of mechanical power for voiding and the bladder outlet as a physical entity that dissipates this power (Pext) in the form of flow rate and pressure during voiding [2, 9].
The detrusor provides the power but the outlet determines how this is split into pressure or flow rate. Therefore, the flow rate and detrusor pressure have an inverse relationship, for a given power of external voiding (Pext), the product of the two must be constant. A high flow suggests a low pressure (normal voiding) and a low flow suggests a high pressure (obstruction). This is graphically represented by the Hill equation and the hyperbolic curve shows the low pressure-high flow and high pressure-low flow voiding relationship (Fig. 2). This represents the bladder-output relation (BOR) and like other muscles, the detrusor has a fundamental relation between the force of contraction (detrusor pressure) and the speed of shortening of the muscle (flow rate) [12]. This inverse relation is an inherent myogenic trait and it is important to recognize that this can only apply when there is a “normal” or given, detrusor muscle power. The curve is not fixed and power can change for a particular detrusor system. Increasing the prestreched length of muscle fibers (to a point) by increasing bladder filling volume increases power and higher flow is possible. And correspondingly, decreasing bladder volume or detrusor decompensation will decrease power. Therefore, it is not only the bladder outlet (FCZ) but also the detrusor power-volume relation that determines peak flow [6]. The Bladder Contractility Index (BCI), discussed further in the following section, is derived from the work by Schafer and categorizes men according to strength of bladder contractility.

This developing understanding of the hydrodynamics of the bladder and bladder outlet resulted in the development of nomograms to objectively categorize male patients with bothersome lower urinary tract symptoms. When the BCI and BOOI nomograms are overlaid, a data point can be categorized in one of nine zones ranging from no obstruction with good contractility to obstruction with weak contractility. These are reviewed in further detail in chapter “Nomograms”. The BOOI and BCI are easy to perform calculations that can help categorize patients according to the results of pressure-flow studies.

In the absence of outlet obstruction or neurologic dysfunction, the voiding phase of urodynamic measurements follows an expected pattern. Once volitional voiding is initiated, the detrusor begins to contract. The pressure generated prior to commencement of urine flow is the pre-micturition pressure and is broadly categorized as an isovolumetric contraction, a contraction that occurs at a consistent volume. The abdominal and intravesical pressures at the onset of flow are recorded and the difference between these values represents the opening detrusor pressure. As detrusor pressure increases, the urethra distends (increasing A of the FCZ) and subsequently flow rate increases to its maximum rate, Q_max. Detrusor pressure at Q_max is also recorded as this is used in identifying conditions of obstruction as discussed previously. As the bladder empties, pressure and flow decrease. The closing pressure, the pressure at which flow stops, is recorded and the voiding phase is complete (Fig. 3).